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1.63 Advanced Fluid Dynamics of the Environment (MIT) 1.63 Advanced Fluid Dynamics of the Environment (MIT)

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year. Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Subjects

fluid dynamics | fluid dynamics | fluid motion | fluid motion | Cartesian tensor convention | Cartesian tensor convention | scaling | scaling | approximations | approximations | slow flow | slow flow | Stokes flow | Stokes flow | Oseen | Oseen | spreading | spreading | gravity | gravity | stratified fluid | stratified fluid | boundary layer | boundary layer | high speed flow | high speed flow | jets | jets | thermal plume | thermal plume | pure fluids | pure fluids | porous media | porous media | similarity method of solution | similarity method of solution | shear | shear | stratification | stratification | Orr-Sommerfeld | Orr-Sommerfeld | capillary phenomena | capillary phenomena | bubbles | bubbles | drops | drops | Marangoni instability | Marangoni instability | contact lines | contact lines | geophysical fluid dynamics | geophysical fluid dynamics | coastal flows | coastal flows | wind-induced flows | wind-induced flows | coastal upwelling | coastal upwelling | transient boundary layer | transient boundary layer | buoyancy | buoyancy | convection porous media | convection porous media | dispersion | dispersion | hydrodynamic instability | hydrodynamic instability | Kelvin-Helmholtz instability | Kelvin-Helmholtz instability

License

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22.615 MHD Theory of Fusion Systems (MIT) 22.615 MHD Theory of Fusion Systems (MIT)

Description

This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta. This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.

Subjects

Magnetohydrodynamics | Magnetohydrodynamics | plasma | plasma | transport theory | transport theory | Boltzmann-Maxwell equations | Boltzmann-Maxwell equations | tokamaks | tokamaks | MHD equilibria | MHD equilibria | poloidal field design | poloidal field design | MHD stability theory | MHD stability theory | Energy Principle | Energy Principle | interchange instability | interchange instability | ballooning modes | ballooning modes | second region of stability | second region of stability | external kink modes | external kink modes | MHD instabilities | MHD instabilities

License

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2.700 Principles of Naval Architecture (MIT) 2.700 Principles of Naval Architecture (MIT)

Description

This course presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. It introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations. This course presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. It introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations.

Subjects

naval architecture | naval architecture | ship geometry | ship geometry | geometry of ships | geometry of ships | ship resistance | ship resistance | flow | flow | hydrostatics | hydrostatics | intact stability | intact stability | damage stability | damage stability | general stability | general stability | hull | hull | hydrostatic | hydrostatic | ship model testing | ship model testing | hull structure | hull structure | Resistance | Resistance | Propulsion | Propulsion | Vibration | Vibration | submarine | submarine | hull subdivision | hull subdivision | midsection | midsection

License

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18.336 Numerical Methods of Applied Mathematics II (MIT) 18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

Linear systems | Linear systems | Fast Fourier Transform | Fast Fourier Transform | Wave equation | Wave equation | Von Neumann analysis | Von Neumann analysis | Conditions for stability | Conditions for stability | Dissipation | Dissipation | Multistep schemes | Multistep schemes | Dispersion | Dispersion | Group Velocity | Group Velocity | Propagation of Wave Packets | Propagation of Wave Packets | Parabolic Equations | Parabolic Equations | The Du Fort Frankel Scheme | The Du Fort Frankel Scheme | Convection-Diffusion equation | Convection-Diffusion equation | ADI Methods | ADI Methods | Elliptic Equations | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | Jacobi | Gauss-Seidel and SOR(w) | ODEs | ODEs | finite differences | finite differences | spectral methods | spectral methods | well-posedness and stability | well-posedness and stability | boundary and nonlinear instabilities | boundary and nonlinear instabilities | Finite Difference Schemes | Finite Difference Schemes | Partial Differential Equations | Partial Differential Equations

License

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1.018J Fundamentals of Ecology (MIT) 1.018J Fundamentals of Ecology (MIT)

Description

This is a basic subject in ecology that seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. The course covers productivity and biogeochemical cycles in ecosystems, trophic dynamics, community structure and stability, competition and predation, evolution and natural selection, population growth and physiological ecology. There is particular emphasis placed on aquatic systems. This is a basic subject in ecology that seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. The course covers productivity and biogeochemical cycles in ecosystems, trophic dynamics, community structure and stability, competition and predation, evolution and natural selection, population growth and physiological ecology. There is particular emphasis placed on aquatic systems.

Subjects

ecology | ecology | flow of energy | flow of energy | flow of materials | flow of materials | ecosystems | ecosystems | distribution and abundance of organisms | distribution and abundance of organisms | productivity cycles | productivity cycles | biogeochemical cycles | biogeochemical cycles | trophic dynamics | trophic dynamics | community structure and stability | community structure and stability | competition and predation | competition and predation | evolution and natural selection | evolution and natural selection | population growth | population growth | physiological ecology | physiological ecology | aquatic systems | aquatic systems | community structure | community structure | community stability | community stability | competition | competition | predation | predation | distribution | distribution | organisms | organisms | evolution | evolution | natural selection | natural selection | energy flow | energy flow | 1.018 | 1.018 | 7.30 | 7.30

License

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22.313 Thermal Hydraulics in Nuclear Power Technology (MIT) 22.313 Thermal Hydraulics in Nuclear Power Technology (MIT)

Description

This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis.Starting in Spring 2007, this course will be offered jointly in the Departments of Nuclear Science and Engineering, Mechanical Engineering, and Chemical Engineering, and will be titled "Thermal Hydraulics in Power Technology." This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis.Starting in Spring 2007, this course will be offered jointly in the Departments of Nuclear Science and Engineering, Mechanical Engineering, and Chemical Engineering, and will be titled "Thermal Hydraulics in Power Technology."

Subjects

reactor | reactor | nuclear reactor | nuclear reactor | thermal behavior | thermal behavior | hydraulic | hydraulic | hydraulic behavior | hydraulic behavior | heat | heat | modeling | modeling | steam | steam | stability | stability | instability | instability | thermo-fluid dynamic phenomena | thermo-fluid dynamic phenomena | single-heated channel-transient analysis | single-heated channel-transient analysis | Multiple-heated channels | Multiple-heated channels | Loop analysis | Loop analysis | single and two-phase natural circulation | single and two-phase natural circulation | Kinematics | Kinematics | two-phase flows | two-phase flows | subchannel analysis | subchannel analysis | Core thermal analysis | Core thermal analysis

License

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18.336 Numerical Methods of Applied Mathematics II (MIT) 18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.

Subjects

Linear systems | Linear systems | Fast Fourier Transform | Fast Fourier Transform | Wave equation | Wave equation | Von Neumann analysis | Von Neumann analysis | Conditions for stability | Conditions for stability | Dissipation | Dissipation | Multistep schemes | Multistep schemes | Dispersion | Dispersion | Group Velocity | Group Velocity | Propagation of Wave Packets | Propagation of Wave Packets | Parabolic Equations | Parabolic Equations | The Du Fort Frankel Scheme | The Du Fort Frankel Scheme | Convection-Diffusion equation | Convection-Diffusion equation | ADI Methods | ADI Methods | Elliptic Equations | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | Jacobi | Gauss-Seidel and SOR(w) | ODEs | ODEs | finite differences | finite differences | spectral methods | spectral methods | well-posedness and stability | well-posedness and stability | boundary and nonlinear instabilities | boundary and nonlinear instabilities | Finite Difference Schemes | Finite Difference Schemes | Partial Differential Equations | Partial Differential Equations

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc. Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | Nonlinear dynamical systems | nonlinear waves | nonlinear waves | diffusion | diffusion | stability | stability | characteristics | characteristics | nonlinear steepening | nonlinear steepening | breaking and shock formation | breaking and shock formation | conservation laws | conservation laws | first-order partial differential equations | first-order partial differential equations | finite differences | finite differences | numerical stability | numerical stability | traffic problems | traffic problems | flows in rivers | flows in rivers | internal waves | internal waves | mechanical vibrations | mechanical vibrations

License

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18.086 Mathematical Methods for Engineers II (MIT) 18.086 Mathematical Methods for Engineers II (MIT)

Description

Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Optimization: network flows | linear programming

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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2.032 Dynamics (MIT) 2.032 Dynamics (MIT)

Description

This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas. This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas.

Subjects

motion | motion | momentum | momentum | work-energy principle | work-energy principle | degrees of freedom | degrees of freedom | Lagrange's equations | Lagrange's equations | D'Alembert's principle | D'Alembert's principle | Hamilton's principle | Hamilton's principle | gyroscope | gyroscope | gyroscopic effect | gyroscopic effect | steady motions | steady motions | nature of small deviations | nature of small deviations | natural modes | natural modes | natural frequencies for continuous and lumped parameter systems | natural frequencies for continuous and lumped parameter systems | mode shapes | mode shapes | forced vibrations | forced vibrations | dynamic stability theory | dynamic stability theory | instability | instability

License

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22.313J Thermal Hydraulics in Power Technology (MIT) 22.313J Thermal Hydraulics in Power Technology (MIT)

Description

This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis. This course covers the thermo-fluid dynamic phenomena and analysis methods for conventional and nuclear power stations. Specific topics include: kinematics and dynamics of two-phase flows; steam separation; boiling, instabilities, and critical conditions; single-channel transient analysis; multiple channels connected at plena; loop analysis including single and two-phase natural circulation; and subchannel analysis.

Subjects

reactor | reactor | nuclear reactor | nuclear reactor | thermal behavior | thermal behavior | hydraulic | hydraulic | hydraulic behavior | hydraulic behavior | heat | heat | modeling | modeling | steam | steam | stability | stability | instability | instability | thermo-fluid dynamic phenomena | thermo-fluid dynamic phenomena | single-heated channel-transient analysis | single-heated channel-transient analysis | Multiple-heated channels | Multiple-heated channels | Loop analysis | Loop analysis | single and two-phase natural circulation | single and two-phase natural circulation | Kinematics | Kinematics | two-phase flows | two-phase flows | subchannel analysis | subchannel analysis | Core thermal analysis | Core thermal analysis

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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22.101 Applied Nuclear Physics (MIT) 22.101 Applied Nuclear Physics (MIT)

Description

The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions. The topics covered under this course include elements of nuclear physics for engineering students, basic properties of the nucleus and nuclear radiations, quantum mechanical calculations of deuteron bound-state wave function and energy, n-p scattering cross-section, transition probability per unit time and barrier transmission probability. Also explored are binding energy and nuclear stability, interactions of charged particles, neutrons, and gamma rays with matter, radioactive decays, energetics and general cross-section behavior in nuclear reactions.

Subjects

Nuclear physics | Nuclear physics | Nuclear reaction | Nuclear reaction | Nucleus | Nucleus | Nuclear radiation | Nuclear radiation | Quantum mechanics | Quantum mechanics | Deuteron bound-state wave function and energy | Deuteron bound-state wave function and energy | n-p scattering cross-section | n-p scattering cross-section | Transition probability per unit time | Transition probability per unit time | Barrier transmission probability | Barrier transmission probability | Binding energy | Binding energy | Nuclear stability | Nuclear stability | Interactions of charged particles neutrons and gamma rays with matter | Interactions of charged particles neutrons and gamma rays with matter | Radioactive decay | Radioactive decay | Energetics | Energetics | nuclear physics | nuclear physics | nuclear reaction | nuclear reaction | nucleus | nucleus | nuclear radiation | nuclear radiation | quantum mechanics | quantum mechanics | deuteron bound-state wave function and energy | deuteron bound-state wave function and energy | transition probability per unit time | transition probability per unit time | barrier transmission probability | barrier transmission probability | nuclear stability | nuclear stability | Interactions of charged particles | Interactions of charged particles | neutrons | neutrons | and gamma rays with matter | and gamma rays with matter | energetics | energetics

License

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1.63 Advanced Fluid Dynamics of the Environment (MIT)

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Subjects

fluid dynamics | fluid motion | Cartesian tensor convention | scaling | approximations | slow flow | Stokes flow | Oseen | spreading | gravity | stratified fluid | boundary layer | high speed flow | jets | thermal plume | pure fluids | porous media | similarity method of solution | shear | stratification | Orr-Sommerfeld | capillary phenomena | bubbles | drops | Marangoni instability | contact lines | geophysical fluid dynamics | coastal flows | wind-induced flows | coastal upwelling | transient boundary layer | buoyancy | convection porous media | dispersion | hydrodynamic instability | Kelvin-Helmholtz instability

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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1.63 Advanced Fluid Dynamics of the Environment (MIT)

Description

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

Subjects

fluid dynamics | fluid motion | Cartesian tensor convention | scaling | approximations | slow flow | Stokes flow | Oseen | spreading | gravity | stratified fluid | boundary layer | high speed flow | jets | thermal plume | pure fluids | porous media | similarity method of solution | shear | stratification | Orr-Sommerfeld | capillary phenomena | bubbles | drops | Marangoni instability | contact lines | geophysical fluid dynamics | coastal flows | wind-induced flows | coastal upwelling | transient boundary layer | buoyancy | convection porous media | dispersion | hydrodynamic instability | Kelvin-Helmholtz instability

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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2.700 Principles of Naval Architecture (MIT)

Description

This course presents principles of naval architecture, ship geometry, hydrostatics, calculation and drawing of curves of form, intact and damage stability, hull structure strength calculations and ship resistance. It introduces computer-aided naval ship design and analysis tools. Projects include analysis of ship lines drawings, calculation of ship hydrostatic characteristics, analysis of intact and damaged stability, ship model testing, and hull structure strength calculations.

Subjects

naval architecture | ship geometry | geometry of ships | ship resistance | flow | hydrostatics | intact stability | damage stability | general stability | hull | hydrostatic | ship model testing | hull structure | Resistance | Propulsion | Vibration | submarine | hull subdivision | midsection

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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22.615 MHD Theory of Fusion Systems (MIT)

Description

This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.

Subjects

Magnetohydrodynamics | plasma | transport theory | Boltzmann-Maxwell equations | tokamaks | MHD equilibria | poloidal field design | MHD stability theory | Energy Principle | interchange instability | ballooning modes | second region of stability | external kink modes | MHD instabilities

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Control (MIT) Control (MIT)

Description

6.241 examines linear, discrete- and continuous-time, and multi-input-output systems in control and related areas. Least squares and matrix perturbation problems are considered. Topics covered include: state-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, minimality, internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, observer-based compensators, measures of control performance, and robustness issues using singular values of transfer functions. Nonlinear systems are also introduced. 6.241 examines linear, discrete- and continuous-time, and multi-input-output systems in control and related areas. Least squares and matrix perturbation problems are considered. Topics covered include: state-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, minimality, internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, observer-based compensators, measures of control performance, and robustness issues using singular values of transfer functions. Nonlinear systems are also introduced.

Subjects

control | control | linear | linear | discrete | discrete | continuous-time | continuous-time | multi-input-output | multi-input-output | least squares | least squares | matrix perturbation | matrix perturbation | state-space models | stability | controllability | observability | transfer function matrices | poles | state-space models | stability | controllability | observability | transfer function matrices | poles | zeros | zeros | minimality | minimality | feedback | feedback | compensators | compensators | state feedback | state feedback | optimal regulation | optimal regulation | observers | transfer functions | observers | transfer functions | nonlinear systems | nonlinear systems | linear systems | linear systems

License

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16.31 Feedback Control Systems (MIT) 16.31 Feedback Control Systems (MIT)

Description

This course covers the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, the student should be able to design controllers using state-space methods and evaluate whether these controllers are robust. This course covers the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, the student should be able to design controllers using state-space methods and evaluate whether these controllers are robust.

Subjects

linear system response | linear system response | aircraft control | aircraft control | frequency response methods | frequency response methods | Nyquist stability theorem | Nyquist stability theorem | bode plots | bode plots | state-space systems | state-space systems | full-state feedback control | full-state feedback control | open-loop estimators | open-loop estimators | closed-loop estimators | closed-loop estimators | robustness analysis | robustness analysis | small gain theorem | small gain theorem

License

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12.804 Large-scale Flow Dynamics Lab (MIT) 12.804 Large-scale Flow Dynamics Lab (MIT)

Description

12.804 is a laboratory accompaniment to 12.803, Quasi-balanced Circulations in Oceans and Atmospheres. The subject includes analysis of observations of oceanic and atmospheric quasi-balanced flows, computational models, and rotating tank experiments. Student projects illustrate the basic principles of potential vorticity conservation and inversion, Rossby wave propagation, baroclinic instability, and the behavior of isolated vortices. 12.804 is a laboratory accompaniment to 12.803, Quasi-balanced Circulations in Oceans and Atmospheres. The subject includes analysis of observations of oceanic and atmospheric quasi-balanced flows, computational models, and rotating tank experiments. Student projects illustrate the basic principles of potential vorticity conservation and inversion, Rossby wave propagation, baroclinic instability, and the behavior of isolated vortices.

Subjects

flow dynamics laboratory | flow dynamics laboratory | oceanic | oceanic | atmospheric | atmospheric | quasi-balanced flows | quasi-balanced flows | computational models | computational models | rotating tank experiments | rotating tank experiments | potential vorticity conservation | potential vorticity conservation | potential vorticity inversion | potential vorticity inversion | Rossby waves | Rossby waves | Rossby wave propagation | Rossby wave propagation | baroclinic instability | baroclinic instability | vortices | vortices

License

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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations | linear algebra | linear algebra | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks

License

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4.440 Basic Structural Theory (MIT) 4.440 Basic Structural Theory (MIT)

Description

This course introduces the static behavior of structures and strength of materials. Topics covered include: reactions, truss analysis, stability of structures, stress and strain at a point, shear and bending moment diagrams, stresses in beams, Mohr's Circle, column buckling, and deflection of beams. Laboratory sessions are included where students are asked to solve structural problems by building simple models and testing them. This course introduces the static behavior of structures and strength of materials. Topics covered include: reactions, truss analysis, stability of structures, stress and strain at a point, shear and bending moment diagrams, stresses in beams, Mohr's Circle, column buckling, and deflection of beams. Laboratory sessions are included where students are asked to solve structural problems by building simple models and testing them.

Subjects

structures | structures | building technology | building technology | construction | construction | static behavior of structures and strength of materials | static behavior of structures and strength of materials | reactions | reactions | truss analysis | truss analysis | stability of structures | stability of structures | stress and strain at a point | stress and strain at a point | shear and bending moment diagrams | shear and bending moment diagrams | stresses in beams | stresses in beams | Mohr's Circle | Mohr's Circle | column buckling | column buckling | deflection of beams | deflection of beams

License

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4.462 Building Technologies II: Building Structural Systems I (MIT) 4.462 Building Technologies II: Building Structural Systems I (MIT)

Description

This course serves as an introduction to the history, theory, and construction of basic structural systems with an introduction to energy issues in buildings. Emphasis is placed on developing an understanding of basic systematic and elemental behavior; principles of structural behavior and analysis of individual structural elements and strategies for load carrying. The subject introduces fundamental energy topics including thermodynamics, psychrometrics, and comfort, as they relate to building design and construction. This course is the first of two graduate structures courses, the second of which is 4.463. They offer an expanded version of the content presented in the undergraduate course, 4.440. This course serves as an introduction to the history, theory, and construction of basic structural systems with an introduction to energy issues in buildings. Emphasis is placed on developing an understanding of basic systematic and elemental behavior; principles of structural behavior and analysis of individual structural elements and strategies for load carrying. The subject introduces fundamental energy topics including thermodynamics, psychrometrics, and comfort, as they relate to building design and construction. This course is the first of two graduate structures courses, the second of which is 4.463. They offer an expanded version of the content presented in the undergraduate course, 4.440.

Subjects

column buckling | and deflection of beams | column buckling | and deflection of beams | Mohr's Circle | Mohr's Circle | stresses in beams | stresses in beams | shear and bending moment diagrams | shear and bending moment diagrams | stress and strain at a point | stress and strain at a point | stability of structures | stability of structures | truss analysis | truss analysis | reactions | reactions | static behavior of structures and strength of materials | static behavior of structures and strength of materials | construction | construction | building technology | building technology | structures | structures | column buckling and deflection of beams | column buckling and deflection of beams

License

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17.884J Collective Choice I (MIT) 17.884J Collective Choice I (MIT)

Description

This is an applied theory course covering topics in the political economy of democratic countries. This course examines political institutions from a rational choice perspective. The now burgeoning rational choice literature on legislatures, bureaucracies, courts, and elections constitutes the chief focus. Some focus will be placed on institutions from a comparative and/or international perspective. This is an applied theory course covering topics in the political economy of democratic countries. This course examines political institutions from a rational choice perspective. The now burgeoning rational choice literature on legislatures, bureaucracies, courts, and elections constitutes the chief focus. Some focus will be placed on institutions from a comparative and/or international perspective.

Subjects

Political science | Political science | economics | economics | political economy | political economy | democratic | democratic | countries | countries | collective | collective | choice | choice | electoral competiton | electoral competiton | public goods | public goods | size | size | government | government | taxation | taxation | income redistribution | income redistribution | macroeconomic policy | macroeconomic policy | voting models | voting models | equilibrium models | equilibrium models | information | information | learning | learning | agency models | agency models | political parties | political parties | vote-buying | vote-buying | vote-trading | vote-trading | resource allocation | resource allocation | Colonel Blotto | Colonel Blotto | interest groups | interest groups | lobbying | lobbying | legislatures | legislatures | bargaining | bargaining | coalitions | coalitions | stability | stability | informational | informational | distributive | distributive | theories | theories | executive | executive | relations | relations | representative democracy | representative democracy

License

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6.302 Feedback Systems (MIT) 6.302 Feedback Systems (MIT)

Description

This course provides an introduction to the design of feedback systems. Topics covered include: properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, root locus method, Nyquist criterion, frequency-domain design, compensation techniques, application to a wide variety of physical systems, internal and external compensation of operational amplifiers, modelling and compensation of power coverter systems and phase lock loops. This course provides an introduction to the design of feedback systems. Topics covered include: properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, root locus method, Nyquist criterion, frequency-domain design, compensation techniques, application to a wide variety of physical systems, internal and external compensation of operational amplifiers, modelling and compensation of power coverter systems and phase lock loops.

Subjects

feedback system | feedback system | time-domain performance | time-domain performance | frequency-domain performance | frequency-domain performance | stability | stability | root locus method | root locus method | Nyquist criterion | Nyquist criterion | frequency-domain design | frequency-domain design | compensation techniques | compensation techniques | internal compensation | internal compensation | external compensation | external compensation | operational amplifiers | operational amplifiers | power coverter systems | power coverter systems | phase lock loops | phase lock loops

License

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12.520 Geodynamics (MIT) 12.520 Geodynamics (MIT)

Description

This course deals with mechanics of deformation of the crust and mantle, with emphasis on the importance of different rheological descriptions: brittle, elastic, linear and nonlinear fluids, and viscoelastic. This course deals with mechanics of deformation of the crust and mantle, with emphasis on the importance of different rheological descriptions: brittle, elastic, linear and nonlinear fluids, and viscoelastic.

Subjects

Geodynamics | Geodynamics | mechanics of deformation | mechanics of deformation | crust | crust | mantle | mantle | rheological descriptions | rheological descriptions | brittle | brittle | elastic | elastic | linear | linear | nonlinear fluids | nonlinear fluids | viscoelastic | viscoelastic | surface tractions | surface tractions | tectonic stress | tectonic stress | quantity expression | quantity expression | stress variations | stress variations | sandbox tectonics | sandbox tectonics | displacement gradients | displacement gradients | strains | strains | rotations | rotations | finite strain | finite strain | motivation | motivation | dislocation | dislocation | plates | plates | topography | topography | rock rheology | rock rheology | accretionary wedge | accretionary wedge | linear fluids | linear fluids | elastic models | elastic models | newtonian fluids | newtonian fluids | stream function | stream function | Rayleigh-Taylor instability | Rayleigh-Taylor instability | diapirism | diapirism | diapirs | diapirs | plumes | plumes | corner flow | corner flow | power law creep | power law creep | viscoelasticity | viscoelasticity | porous media | porous media | Elsasser model | Elsasser model | time dependent porous flow | time dependent porous flow

License

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